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//Autor: Bartłomiej Czarkowski
#include <bits/stdc++.h>

using namespace std;

const int N = 101'000;
int n;
int dp[N][3];
char s[N];

int daj(int x) {
	if (!x) {
		return 0;
	}
	return max(1, x - 1);
}

void solve() {
	scanf("%d%s", &n, s + 1);
	
	int lf = 1;
	while (s[lf] == '0' && lf < n) {
		++lf;
	}
	
	if (lf == n && s[n] == '0') {
		printf("0\n");
		return;
	}
	
	int rg = n;
	while (s[rg] == '0') {
		--rg;
	}
	
	vector <int> v1, v2;
	
	int ost = lf;
	for (int i = lf + 1; i <= rg; ++i) {
		if (s[i] == '1') {
			v1.push_back(i - ost - 1);
			ost = i;
		}
	}
	
	v2.push_back(lf - 1);
	v2.push_back(n - rg);
	
	sort(v1.begin(), v1.end());
	reverse(v1.begin(), v1.end());
	
	sort(v2.begin(), v2.end());
	reverse(v2.begin(), v2.end());
	
	int m = v1.size();
	for (int i = 0; i <= m; ++i) {
		for (int j = 0; j <= 2; ++j) {
			dp[i][j] = -1e9;
		}
	}
	dp[0][0] = 0;
	dp[0][1] = v2[0];
	dp[0][2] = v2[0] + max(0, v2[1] - 1);
	for (int i = 1; i <= m; ++i) {
		dp[i][0] = dp[i - 1][0] + daj(max(0, v1[i - 1] - (i - 1) * 4));
		for (int j = 1; j <= 2; ++j) {
			dp[i][j] = max(dp[i - 1][j] + daj(max(0, v1[i - 1] - (i - 1) * 4 - j * 2)),
							dp[i][j - 1] + max(0, v2[j - 1] - i * 2 - (j - 1)));
		}
	}
	printf("%d\n", n - dp[m][2]);	
}

int main() {
	int q=1;
	scanf("%d", &q);
	while(q--) {
		solve();
	}
	return 0;
}